Theme Essential Question: How can you use numerical and algebraic expressions, equations, and inequalities to solve real-life mathematical problems?
Essential Questions:
How does the solution of an inequality, in the context of a problem, represent the feasible outcomes?
Why does the inequality change from greater to least or least to greater when multiplying of dividing a negative number?
Standards:
7. EE.4b Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example, as a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.
Objectives:
The student will solve inequalities that involve one operation.
The student will graph the solution set for given inequalities.
The student will provide a viable argument to justify the inequality symbol changing directions when multiplying or dividing by a negative number.
The student will solve real-world problems using inequalities.
Background Information Recommended: For a quick overview of the standard(s) to be addressed in this lesson, see Arizona’s Content Standards Reference Materials at http://www.azed.gov/educator-certification/
Taken from Ohio Dept of Education Mathematics Model Curriculum 6-28-2022 Provide multiple opportunities for students to work with multi-step problem situations that have multiple solutions and therefore can be represented by an inequality. Students need to be aware that values can satisfy an inequality but not be appropriate for the situation, therefore limiting the solutions for that particular problem.
Assessment: Product
The students will be designing two separate “I have… who has..” card game that will include problems from unit-lesson 2-2 to unit-lesson 2-4 with supporting word problems. The first game will deal with equalities and the second will deal with inequalities.
Students should be placed into small groups.
Each group is to design several cards representing the work addressed during these lessons.
The games are exchanged between groups and played.
Key Questions
How do you solve inequalities that involve one operation?
How do graph the solution set of the inequality and interpret it in the context of the problem?
How do you describe the solution set in the context of a problem?
How do you justify changing the direction of the inequality symbol when multiplying or dividing by a negation number?
Observable Student Behaviors
The student can solve a one operation inequality and explain the feasibility of the solution.
The student can graph the solution to a one operation inequality and explain the feasibility of the solution.
The student can provide a viable argument to justify the direction change of an inequality symbol when multiplying or dividing by a negation number.
Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.
Houghton Mifflin On Core Mathematics Middle School Grade 7, Unit 3-4, p. 69-72
ABC Mastering the Common Core in Mathematics
Graphing Inequalities, Chapter 9.6, p. 105-106
Solving Inequalities by Addition and Subtraction, Chapter 9.7, p. 107
Solving Inequalities by Multiplication and Division, Chapter 9.8, p.108
Gizmo
Solving Linear Inequalities using Addition and Subtraction
Solve a linear inequality. Graph the solution on a dynamic number line.
Solving Linear Inequalities using Multiplication and Division
Solve an inequality involving multiplication and division. Graph the solution on a number line.
Highly Recommended – Problem associated with 7.EE.4b is found in the next lesson 2-4.
The Illustrative Mathematics Project offers guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience in a faithful implementation of the Common Core State Standards. The website features a clickable version of the Common Core in mathematics and the first round of "illustrations" of specific standards with associated classroom tasks and solutions.
JBHM 8th, GP 2, p. 133-176
Glencoe 7th Grade Mathematics Application and Concepts Course 4, p. 172-175,
Glencoe 7th Grade PreAlgebra, Chapter 7-3 to 7-5, p. 339-354
Lesson Plan in Word Format (Click Cancel if asked to Log In) Resources:
Professional Texts:
Literary Texts
Mathematics in Children's Literature:
Many children's books include math concepts and can be used to help teach them in a fun way. This website includes several annotated Lists of Children's Literature including the math concepts and grade levels. Click on the following link, http://libguides.nl.edu/mathinchildrenslit, and then look under Math and Literature Bibliographies.
Connect Four game format: Students play a generalized version of connect four, gaining the chance to place a piece on the board by answering arithmetic questions (addition, subtraction, multiplication, division). Parameters: time, difficulty level, types of questions. Arithmetic Four is one of the Interactivate assessment games.
Connect Four game format: Students play a generalized version of connect four, gaining the chance to place a piece on the board by answering arithmetic questions (addition, subtraction, multiplication, division).
Parameters: time, difficulty level, types of questions. Arithmetic Four is one of the Interactivate assessment games.
Related Topics: addition, arithmetic, assessment, division, integers, multiplication, negative number, positive number, positive part of the operand, subtraction, whole numbers
Related Topics: addition, arithmetic, assessment, division, integers, multiplication, negative number,
positive number, positive part of the operand, subtraction, whole numbers
Smartboard Lesson, Promethean Lessons
ALGEBRAIC EXPRESSIONS MILLIONAIRE
http://www.math-play.com/Algebraic-Expressions-Millionaire/algebraic-expressions-millionaire.html This Algebraic Expressions Millionaire Game can be played online alone or in two teams. For each question you have to identify the correct mathematical expression that models a given word expression. You could also use it as classroom challenge and have students write their answers on white board and check.
Content: Solving One-Step Inequalities
Theme Essential Question:
How can you use numerical and algebraic expressions, equations, and inequalities to solve real-life mathematical problems?
Essential Questions:
Standards:
Objectives:
Background Information
Recommended: For a quick overview of the standard(s) to be addressed in this lesson, see Arizona’s Content Standards Reference Materials at http://www.azed.gov/educator-certification/
Taken from Ohio Dept of Education Mathematics Model Curriculum 6-28-2022
Provide multiple opportunities for students to work with multi-step problem situations that have multiple solutions and therefore can be represented by an inequality. Students need to be aware that values can satisfy an inequality but not be appropriate for the situation, therefore limiting the solutions for that particular problem.
Assessment:
Product
Key Questions
Observable Student Behaviors
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Vocabulary:
Inequalities
Inequality signs
Algebraic expressions
Inverse operations
Solution set
Suggested Activities:
- Houghton Mifflin On Core Mathematics Middle School Grade 7, Unit 3-4, p. 69-72
- ABC Mastering the Common Core in Mathematics
- Graphing Inequalities, Chapter 9.6, p. 105-106
- Solving Inequalities by Addition and Subtraction, Chapter 9.7, p. 107
- Solving Inequalities by Multiplication and Division, Chapter 9.8, p.108
Gizmo- Solving Linear Inequalities using Addition and Subtraction
Solve a linear inequality. Graph the solution on a dynamic number line.- Solving Linear Inequalities using Multiplication and Division
Solve an inequality involving multiplication and division. Graph the solution on a number line.- Highly Recommended – Problem associated with 7.EE.4b is found in the next lesson 2-4.
The Illustrative Mathematics Project offers guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience in a faithful implementation of the Common Core State Standards. The website features a clickable version of the Common Core in mathematics and the first round of "illustrations" of specific standards with associated classroom tasks and solutions.Diverse Learners
Homework: (Teacher Discretion)
Terminology for Teachers:
Ethnicity/Culture | Immigration/Migration | Intercultural Competence | Socialization | Racism/Discrimination
High Yield Strategies
Similarities/Differences | Summarizing/Notetaking | Reinforcing/Recognition | Homework/Practice |
Non-Linguistic representation | Cooperative Learning | Objectives/Feedback |
Generating-Testing Hypothesis | Cues, Questions, Organizers
Resources:
Professional Texts:
Literary Texts
- Mathematics in Children's Literature:
Many children's books include math concepts and can be used to help teach them in a fun way.This website includes several annotated Lists of Children's Literature including the math concepts and grade levels.
Click on the following link, http://libguides.nl.edu/mathinchildrenslit, and then look under Math and Literature Bibliographies.
- Middle & High School: Literature in Mathematics
Many books include websites with lesson ideas.http://sci.tamucc.edu/~eyoung/middle_school_literature.html
- Lesson Plans for Using Literature in Middle and High School Mathematics (developed by Leonor and edited by Elaine)
http://sci.tamucc.edu/~eyoung/Literature%20webpages/Leonor/index.html- Miscellaneous Math and Children's Literature
http://sci.tamucc.edu/~eyoung/literature.htmlInformational Texts
Art, Music, and Media
Manipulatives
Games
- http://www.math-play.com/Fractions-Jeopardy/fractions-jeopardy.html
Connect Four game format:Students play a generalized version of connect four, gaining the chance to place a piece on the board by answering arithmetic questions (addition, subtraction, multiplication, division). Parameters: time, difficulty level, types of questions. Arithmetic Four is one of the Interactivate assessment games.
- http://www.mathchimp.com/7thGrade.php
- http://www.sumdog.com/ A variety of games covering many math topics
- http://www.mathplayground.com/SMP_index.html
Connect Four game format:Students play a generalized version of connect four, gaining the chance to place a piece on the board by answering arithmetic questions (addition, subtraction, multiplication, division).
Videos
- Discovery Learning http://www.discoveryeducation.com/
- The Teaching Channel
The teaching Channel currently offers videos of K-12 mathematics teaching aligned with theCommon Core Sate Standards, which would be perfect for professional development with
teacher teams.
https://www.teachingchannel.org/videos?categories=topics common-core
- Related Topics: addition, arithmetic, assessment, division, integers, multiplication, negative number,
positive number, positive part of the operand, subtraction, whole numbersSmartboard Lesson, Promethean Lessons
- ALGEBRAIC EXPRESSIONS MILLIONAIRE
http://www.math-play.com/Algebraic-Expressions-Millionaire/algebraic-expressions-millionaire.htmlThis Algebraic Expressions Millionaire Game can be played online alone or in two teams. For each question you have to identify the correct mathematical expression that models a given word expression. You could also use it as classroom challenge and have students write their answers on white board and check.
Other Activities, etc.
- http://www.mathgoodies.com/lessons/vol5/division.html
- http://www.math.com/school/subject1/lessons/S1U1L12GL.html
- Interactivate is a set of free, online courseware for exploration in science and mathematics. It is
- comprised of activities, lessons, and discussions. The site is structured around collections of
activities, lessons, and discussions.Language
Arts
Week 1
Week 2
Week 3
Week 4
Week 5
Week 6
7 Matrix
Accelerated 7
Matrix
Week 1
Week 2
Week 3
Week 4
Week 5
Week 6
Home K-2
Home 3-6
Home 6-8
Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6